Conditions on distance functions that allow to preserve various properties of limit for reals were considered even before the notion of a metric space was introduced. We refer to articles [1]}, [2]}, [3]}, [4]} which contain developments in this direction (see also  [5]}, [6]} and references therein).
Below we present several types of sufficient conditions for an \(EDM\) -distance space to be Hausdorff.
